LESSON 10

The Number of Unmoved Movers

  Chapter 8: 1073b 17-1074b 14

             1082. Now Eudoxus claimed that the motion both of the sun and of the moon involves for each three spheres. The first of these is the sphere of the stars whose positions remain unchanged; the second, the one which passes through the middle of the zodiac; and the third, the one which moves obliquely in the latitude of the animals in the zodiac. But the circle in which the moon is moved is inclined at a greater angle than that in which the sun is moved. He also claimed that the motion of the wandering stars involves four spheres for each. The first and second of these are the same as those mentioned above. The sphere of the fixed stars is the one which imparts motion to all of the spheres, and the sphere which is situated below this and moves through the middle of the zodiac is common to all of the planets. The third sphere for each of the planets has its poles in the circle which passes through the middle signs of the zodiac; and the motion of the fourth sphere is in a circle which is inclined at a greater angle to the middle of this sphere; and while the poles of the third sphere are peculiar to each of the other planets, those of Venus and of Mercury are the same.

             1083. And Callippus assumed the position of the spheres to be the same as Eudoxus did, i.e., as regards the arrangement of their distances, and he gave the same number of spheres to Jupiter and to Saturn as Eudoxus did. But he thought that two spheres should be added both to the sun and to the moon if appearances are to be saved. And to each of the other planets he added one sphere. However, if all spheres taken together are to account for appearances, there must be additional spheres for each of the other planets, one less in number than those mentioned above, which revolve the planets and always restore to the same place the first sphere of the star which is next in order below. For only in this way can all the spheres account for the motion of the planets. Therefore, since, as regards the spheres in which the planets themselves are carried along, some are eight in number and others twenty-five in number, and of these only those in which the lowest planet is carried along do not need to be revolved, then the spheres which revolve the first two planets will be six in number, and those which revolve the last four will be sixteen in number. The total number of spheres, then, both those which carry the planets along and those which revolve them, will be fifty-five. And if one has not added to the moon and to the sun the motions which we have mentioned (1083), the total number of spheres will be forty-seven. Let the number of the spheres, then, be so many.

             1084. Hence it is reasonable to suppose that there are as many substances and immovable principles and perceptible principles. Therefore the statement of necessity is to be left to more powerful thinkers.

             1085. However, if there can be no celestial motion which is not related to the motion of a star, and further if every nature and substance which is unchangeable and has in itself reached the highest good must be thought to be an end, there will be no other nature besides these; but this must be the number of substances. For if there were others, they would cause motion as being ends of local motion.

             1086. But there cannot be other motions besides those mentioned. And it is reasonable to suppose this from the bodies that are moved. For if everything which moves exists by nature for the sake of that which is moved, and all motion is the motion of something moved, no motion will exist for itself or for the sake of another motion, but all motions will exist for the sake of the stars. For if one motion should exist for the sake of another, the latter must also exist for the sake of another. Hence, since an infinite regress is impossible, the end of every motion must be one of the divine bodies which move about in the heavens.

             1087. And it is evident that there is only one heaven. For if there were many heavens, as there are many men, the principle of each would be one in species but many in number. But all things which are many in number have matter; for many individuals have one and the same intelligible structure, for example, man, whereas Socrates is one; but the primary quiddity has no matter, for it is complete reality. Therefore the first mover, which is immovable, is one both in its intelligible structure and in number; and therefore what is moved eternally and continuously is only one. Hence there is only one heaven.

             1088. Now traditions have been handed down from our predecessors and the ancient thinkers, and left to posterity in the form of a myth, that these heavenly bodies are gods, and that the divine encompasses the whole of nature. But the rest of the traditions have been added later in the form of a myth for the persuasion of the multitude, the general welfare, and the passing of laws (172). For they say that the gods have human form and are similar to some of the other animals; and they add other statements which follow upon these and are similar to the ones mentioned. Now if anyone will separate these statements and accept only the first, that they thought the first substances to be gods, this will be considered to be a divine statement. And though every art and every philosophy has often been discovered and again lost, the opinions of these early thinkers have been preserved as relics to the present day. Therefore the opinions of our forefathers and those which have come down to us from the first thinkers are evident only to this extent.

COMMENTARY

             2567. Aristotle states the opinions which the astronomers of his time held about the number of planetary motions. First (1082:C 2567), he gives the opinion of Eudoxus; and second (1083:C 2578), that of Callippus ("And Callippus").

             Now in regard to the first opinion it must be understood that Plato, in attributing unfailing circularity and order to the celestial motions, made mathematical hypotheses by which the apparent irregular motions of the planets can be explained; for he claimed that the motions of the planets are circular and arranged in an orderly way. And the Pythagoreans, with a view to putting into due order the irregularity which appears in the planetary motions on account of their standing still and moving backwards, and their rapidity and slowness, and their apparent differences in size, claimed that the motions of the planets involve eccentric spheres and small circles which they called epicycles; and Ptolemy also subscribes to this view.

             2568. However, something contrary to the points demonstrated in the philosophy of nature seems to follow from this hypothesis; for not every motion will be either towards or away from or around the center of the world. Furthermore it follows that a sphere containing an eccentric sphere either is not of equal density, or there is a vacuum between one sphere and another, or there is some body besides the substance of the spheres that lies between them which will not be a circular body and will have no motion of its own.

             2569. Further, from the hypothesis of epicycles it follows either that the sphere by which the epicycle is moved is not whole and continuous, or that it is divisible, expansible and compressible in the way in which air is divided, expanded and compressed when a body is moved. It also follows that the body itself of a star is moved by itself and not merely by the motion of an orb; and that from the motion of the celestial bodies there will arise the sound about which the Pythagoreans agreed.

             2570. Yet all conclusions of this kind are contrary to the truths established in the philosophy of nature. Therefore Eudoxus, seeing this and seeking to avoid it, claimed that for each planet in the world there are many concentric spheres, each of which has its proper motion, and that as a result of all of these motions the observable motion of the planets is accounted for. Hence Eudoxus held that the motion of the sun as well as that of the moon involves three spheres.

             2571. For the first motion of the sun as well as that of the moon, which is the daily motion, is that by which they are moved from east to west; and he calls this motion "that of the stars whose positions remain unchanged," i.e., of the stars which do not wander, namely, the fixed stars; for, as was said above (C 2558), since the motion of the fixed stars, which is from west to east, was not yet discovered to be contrary to the first motion, it was thought that the daily motion was proper to the eighth sphere, which is the sphere of the fixed stars. It was not thought, however, that the first sphere alone might be sufficient to move all the spheres of the planets by a daily motion, as Ptolemy assumed; but he thought that each planet had its own sphere which would move it by a daily motion. Therefore with a view to explaining this motion he posited a first sphere for both the sun and the moon.

             2572. He also posited a second sphere to account for the motion of the sun and the moon. This passes through the middle of the zodiac with what is called "longitudinal motion," according to which both the sun and the moon are moved from west to east in an opposite direction to the motion of the firmament.

             2573. He posited a third sphere to account for the oblique motion across the latitude of the animals symbolized in the zodiac, inasmuch as a planet sometimes seems to be farther south and sometimes farther north of the middle line of the zodiac. But this motion is more apparent and has a broader spread in the case of the moon than in that of the sun. Hence he adds that the motion by which the moon is carried along is inclined at a greater angle than the sun's motion. And Ptolemy attributed latitudinal motion to the moon but not to the sun. Hence Eudoxus posited a third motion, as Simplicius says, because he thought that the sun also deviated from the middle line of the zodiac towards the two poles; and he made this assumption because the sun does not always rise in the same place during the summer solstice and during the winter solstice. But if it returned in latitude and in longitude at the same time by means of the declination of the great circle [i.e., the ecliptic] along which the sun travels, one sphere would suffice for this. Since this is not the case, however, but it passes through its course in longitude at one time and returns in latitude at another time, for this reason it was necessary to posit a third sphere. And he claimed that this third sphere of the sun is moved in the same direction as the second sphere, but about a different axis and on different poles. He also claimed that this third sphere of the moon is moved in the same direction as the first sphere. But in each case he claimed that the motion of this third sphere was slower than that of the second.

             2574. And he claimed that the motion of each of the other five planets involves four spheres, with the first and second sphere of each planet having the same function as the first and second sphere of the sun and of the moon; because the first motion, which he assumed to be that of the fixed stars, and the second motion, which passes in longitude through the middle line of the zodiac, appear to be common to all the planets.

             2575. Next, he posited a third sphere for each of the planets in order to account for their latitudinal motion, and he assumed that the poles about which it is revolved were located in the middle line of the zodiac. But since he claimed that all spheres are concentric, it would follow from this that the zodiac would pass through the poles of the great circle of the third sphere, and it would follow in the opposite way that the great circle of the third sphere would pass through the poles of the zodiac. Hence it would follow that the motion of the third sphere would carry a planet right up to the poles of the zodiac, which is never seen to occur.

             2576. Therefore he had to posit a fourth sphere, which is the one that would carry the planet, and it would revolve in an opposite direction to the third sphere, namely, from east to west, in equal time, so as to prevent the planet from being diverted farther in latitude from the zodiac. This is what Aristotle means when he says that Eudoxus claimed that the fourth motion of the star is in a circle inclined at an angle to the middle of the third sphere, i.e., to its great circle.

             2577. Therefore, if he posited four spheres for each of the five planets, it follows that there would be twenty spheres for these five planets. And if the three spheres of the sun and the three spheres of the moon are added to this number, there will be twenty-six spheres in all, granted that the body of each planet is understood to be fastened to the last of its own spheres.

             2578. And Callippus assumed (1083).

             Then he gives the opinion of Callippus about the number of spheres. Now Callippus, as Simplicius tells us, was associated with Aristotle at Athens when the discoveries of Eudoxus were corrected and supplemented by him. Hence Callippus maintained the same theory of the spheres as Eudoxus did; and he explained the positions of the spheres by the arrangement of their distances, because he gave to the planets and to their motions and spheres the same order as Eudoxus did.

             2579. And he agreed with Eudoxus as to the number of spheres of Jupiter and Saturn, because he assigned four spheres to each of these; but Callippus thought that two spheres must be added both to the sun and to the moon, if one wants to adopt a theory about them which accords with their motions. He seems to have added these two spheres in order to account for the rapidity and slowness which appears in their motions. The sun would then have five spheres, and the moon likewise would have five. He also added one sphere to each of the remaining planets--Mars, Venus and Mercury--thus giving each of them also five spheres. Perhaps they added this fifth sphere to account for the backward motion and the standing still which appear in these stars. These spheres are called deferent spheres, then, because the body of a planet is carried along by them.

             2580. But in addition to these spheres they posited others, which they called revolving spheres. It would appear that they were led to posit these because the last sphere of a higher planet, for example, of Saturn, must share in the motion of all the higher planets, so that its motion gets away somewhat from that of the first sphere. Hence the first sphere of Jupiter, whose poles are fastened in some way to the highest sphere of Saturn, shared to some extent in the motion of the spheres of Saturn, and thus it was not moved uniformly by the daily motion like the first sphere of Saturn. Therefore it seemed necessary to posit another sphere which revolves this first sphere in order to restore the speed which it loses because of the higher planets. And by the same reasoning it was necessary to posit another sphere which revolves the second sphere of Jupiter, and a third sphere which revolves the third sphere of Jupiter. But it was unnecessary to posit another sphere which revolves the fourth sphere, because the motion of the first sphere, to which the star is fixed, must be composed of all the higher motions. Hence Jupiter has four deferent spheres and three revolving spheres. And in a similar way the other planets have as many revolving spheres, minus one, as deferent spheres.

             2581. Therefore he says that, if all spheres taken together must account for and explain the apparent motion of the planets, it is necessary to posit, in addition to the deferent spheres mentioned above, other spheres, one less in number, which revolve and restore to the same place the first sphere of the star next in order below; for only in this way can the motions of the planets accord with all appearances.

             2582. Therefore, since the deferent spheres which belong to Saturn and to Jupiter are eight in number, because each is assumed to have four spheres; and since those which belong to the other five planets are twenty-five in number, because each of these has five spheres, and of these only those at the end which carry and regulate the star are not revolved, it follows that the revolving spheres of the first two planets, i.e., of Saturn and Jupiter, are six in number, and that those of the last four planets are sixteen in number. But since after Saturn and Jupiter there are five other planets, he evidently omits one of them, i.e., either Mars or Mercury, so that his statement regarding the last four refers to the four lowest; or he omits the moon, so that he refers to the four planets immediately following. Now he omits this either by error, which sometimes happens in the case of numbers, or for some reason which is unknown to us; because the writings of Callippus are not extant, as Simplicius tells us. Hence the total number of deferent spheres and of revolving spheres together is fifty-five.

             2583. But because the difficulty could arise whether it is necessary to add two spheres to the sun and two to the moon, as Callippus did, or whether only two spheres must be given to each, as Eudoxus claimed, he therefore says that, if one does not add two motions to the sun and two to the moon, as Callippus did, it follows that the total number of spheres will be forty-seven; for four deferent spheres would then be subtracted from the above number--two for the sun and two for the moon--and also the same number of revolving spheres; and when eight is subtracted from fifty-five, forty-seven remains.

             2584. But it must be noted that, if above (1083:C 2582), when he said that the revolving spheres of the last four planets are sixteen in number, he omitted the moon, then if two deferent spheres are subtracted from the moon and two from the sun, four revolving spheres are not subtracted but only two, granted that the spheres of the moon do not have revolving spheres; and thus six spheres are subtracted from the first number of spheres, i.e., four deferent and two revolving spheres; and then it follows that the total number of spheres is forty-nine. Hence it seems that Aristotle did not wish to omit the moon but rather Mars, unless one says that Aristotle had forgotten that he had assigned revolving spheres to the moon, and that this is the reason the mistake was made, which does not seem likely.

             2585. Last, he draws his conclusion that the number of spheres is that mentioned.

             2586. Hence it is reasonable (1084).

             Then he infers the number of immaterial substances from the number of celestial motions; and in regard to this he does three things. First (1084:C 2586), he draws the conclusion at which he aims. Second (1085:C 2587), he rejects certain suppositions which could weaken the foregoing inference ("However, if there can be"). Third (1088:C 2597), he compares the points demonstrated about separate substance with the opinions of the ancients and with the common opinions held about these things during his own time ("Now traditions have").

             He says, first (1084), that, since the number of celestial spheres and the number of celestial motions is as has been stated, it is reasonable to suppose that there are the same number of immaterial substances and immobile principles, and even the same number of "perceptible principles," i.e., celestial bodies. He uses the term reasonable in order to imply that this conclusion is a probable one and not one that is necessary. Hence he adds that he is leaving the necessity of this to those who are stronger and more capable of discovering it than he is.

             2587. However, if there can be (1085).

             Here the Philosopher rejects those suppositions by which the conclusion given above could be weakened; and there are three of these. The first is that one could say that there are certain separate substances to which no celestial motion corresponds.

             2588. In order to reject this he says that, if there can be no celestial motions which are not connected with the motion of some star, and again if every immutable substance which has reached "in itself the highest good," i.e., which has reached its own perfection without motion, must be considered an end of some motion, there will be no immutable and immaterial nature besides those substances which are the ends of celestial motions; but the number of separate substances will correspond necessarily to the number of celestial motions.

             2589. Yet the first assumption is not necessary, namely, that every immaterial and immutable substance is the end of some celestial motion. For it can be said that there are separate substances too high to be proportioned to the celestial motions as their ends. And this is not an absurd supposition. For immaterial substances do not exist for the sake of corporeal things, but rather the other way around.

             2590. But there cannot be (1086).

             Then he rejects the second supposition which could weaken the inference mentioned above. For one could say that there are many more motions in the heavens than have been counted, but that these cannot be perceived because they produce no diversity in the motion of one of the celestial bodies which are perceived by the sense of sight and are called stars.

             2591. And in order to reject this he had already equivalently said that there can be no celestial motion which is not connected with the motion of some star. His words here are that there cannot be other motions in the heavens besides those which produce the diversity in the motions of the stars, whether they be the motions mentioned or others, either the same in number or more or fewer.

             2592. This can be taken as a probable conclusion from the bodies which are moved; for if every mover exists for the sake of something moved, and every motion belongs to something which is moved, there can be no motion which exists for itself or merely for the sake of another motion, but all motions must exist for the sake of the stars. For otherwise, if one motion exists for the sake of another, then for the same reason this motion also must exist for the sake of another. Now since an infinite regress is impossible, it follows that the end of every motion is one of the celestial bodies which are moved, as the stars. Hence there cannot be any celestial motion as a result of which some diversity in a star cannot be perceived.

             2593. And it is evident (1087).

             Then he rejects a third supposition by which the above inference could be weakened. For someone might say that there are many worlds, and that in each of these there are as many spheres and motions as there are in this world, or even more, and thus it is necessary to posit many immaterial substances.

             2594. He rejects this position by saying that there is evidently only one heaven. If there were many numerically and the same specifically, as there are many men, a similar judgment would also have to be made about the first principle of each heaven, which is an immovable mover, as has been stated (1079:C 2555). For there would have to be many first principles which are specifically one and numerically many.

             2595. But this view is impossible, because all things which are specifically one and numerically many contain matter. For they are not differentiated from the viewpoint of their intelligible structure or form, because all the individuals have a common intelligible structure, for example, man. It follows, then, that they are distinguished by their matter. Thus Socrates is one not only in his intelligible structure, as man, but also in number.

             2596. However, the first principle, "since it is a quiddity," i.e., since it is its own essence and intelligible structure, does not contain matter, because its substance is "complete reality," i.e., actuality, whereas matter is in potentiality. It remains, then, that the first unmoved mover is one not only in its intelligible structure but also in number. Hence the first eternal motion, which is caused by it, must be unique. It therefore follows that there is only one heaven.

             2597. Now traditions (1088).

             He shows how the points discovered about an immaterial substance compare with both the ancient and common opinions. He says that certain traditions about the separate substances have been handed down from the ancient philosophers, and these have been bequeathed to posterity in the form of a myth, to the effect that these substances are gods, and that the divine encompasses the whole of nature. This follows from the above points, granted that all immaterial substances are called gods. But if only the first principle is called God, there is only one God, as is clear from what has been said. The rest of the tradition has been introduced in the form of a myth in order to persuade the multitude, who cannot grasp intelligible things, and inasmuch as it was expedient for the passing of laws and for the benefit of society, that by inventions of this kind the multitude might be persuaded to aim at virtuous acts and avoid evil ones. He explains the mythological part of this tradition by adding that they said that the gods have the form of men and of certain other animals. For they concocted the fables that certain men as well as other animals have been turned into gods; and they added certain statements consequent upon these and similar to the ones which have just been mentioned. Now if among these traditions someone wishes to accept only the one which was first noted above, namely, that the gods are immaterial substances, this will be considered a divine statement, and one that is probably true. And it is so because every art and every philosophy has often been discovered by human power and again lost, either because of wars, which prevent study, or because of floods or other catastrophes of this kind.

             2598. It was also necessary for Aristotle to maintain this view in order to save the eternity of the world. For it was evident that at one time men began to philosophize and to discover the arts; and it would seem absurd that the human race should be without these for an infinite period of time. Hence he says that philosophy and the various arts were often discovered and lost, and that the opinions of those ancient thinkers are preserved as relics up to the present day.

             2599. Last, he concludes that "the opinion of our forefathers," i.e., the one received from those who philosophized and after whom philosophy was lost, is evident to us only in this way, i.e., in the form of a myth, as has been stated above (1088:C 2597).